please help me i dont get it

Answer: $97.20

Explanation:

Convert 60w(x5 because he has 5 bulbs) and 240w to kw to get 0.3kw and 0.24kw and add these together to get 0.54kw. Next multiply 0.54kw with 4 for 4 hours which is 2.16kw then multiply this by 30 to get 64.8kw. Finally multiply 64.8kw by 1.50 to get $97.20

The total bill for 30 days would be $259.20, considering the energy consumed by the bulbs and water heater. We need to calculate the energy consumed by the bulbs and water heater in kilowatt-hours (kWh) and multiply it by the cost per kWh. The energy consumed by the bulbs is 4800Wh per day and the energy consumed by the water heater is 960Wh per day.

To calculate the bill for 30 days, we need to determine the total energy consumed by the bulbs and water heater in kilowatt-hours (kWh) and then multiply it by the cost per kWh.

The energy consumed by the bulbs can be calculated as follows:

Total energy = power of one bulb * number of bulbs * time = 60W * 5 * 4 hours/day = 1200W * 4 hours/day.

So, the total energy consumed by the bulbs each day is 4800Wh.

The energy consumed by the water heater can be calculated as follows:

Energy = power * time = 240W * 4 hours/day.

So, the total energy consumed by the water heater each day is 960Wh.

To convert it to kWh, divide by 1000:

Total energy consumed each day = (4800 + 960)Wh / 1000 = 5.76kWh.

Finally, calculate the total bill for 30 days:

Total bill = total energy consumed each day * cost per kWh * number of days = 5.76kWh * $1.50/kWh * 30 days = $259.20.

Answer:

1.75 N

Explanation

centripetal force = mass × centripetal acceleration

                            =  0.35×5

                               =  1.75 N

Centripetal force is 1.75N

Therefore.

Centripetal force = mass*centripetal acceleration

                              = 0.35*5

                              =  1.75N

Hence , the centripetal force is 1.75N

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The first ball reaches the ground first

Explanation:

We can solve the problem by using suvat equations, since the motion of both balls is a free fall motion (with constant acceleration, [tex]g=9.8 m/s^2[/tex], towards the ground).

The equation of motion that represents the y-position of the first ball at time t is

[tex]y_1 = u_1 t + \frac{1}{2}at^2[/tex]

where

[tex]u_1 = 41.67 m/s[/tex] is the initial vertical velocity of the ball

[tex]a=-g=-9.8 m/s^2[/tex] is the acceleration (downward, therefore negative)

Substituting [tex]y_1 = 0[/tex] and solving for t, we find the corresponding time at which the ball reaches the ground:

[tex]0=u_1 t + \frac{1}{2}at^2\\0=t(u_1 + \frac{1}{2}at)[/tex]

The two solutions are:

t = 0 (starting moment)

[tex]u_1 + \frac{1}{2}at=0\\t=-\frac{2u_1}{a}=-\frac{2(41.67)}{-9.8}=8.5 s[/tex]

So, the first ball reaches the ground after 8.5 s.

Similarly, for the second ball

[tex]y_2 = u_2 t + \frac{1}{2}at^2[/tex]

where

[tex]u_2 = 55.56 m/s[/tex] is the initial vertical velocity of the ball

[tex]a=-g=-9.8 m/s^2[/tex] is the acceleration (downward, therefore negative)

Substituting [tex]y_2 = 0[/tex] and solving for t, we find the corresponding time at which the ball reaches the ground:

[tex]0=u_2 t + \frac{1}{2}at^2\\0=t(u_2 + \frac{1}{2}at)[/tex]

The two solutions are:

t = 0 (starting moment)

[tex]u_2 + \frac{1}{2}at=0\\t=-\frac{2u_2}{a}=-\frac{2(55.56)}{-9.8}=11.3 s[/tex]

So, the second ball reaches the ground after 11.3 s. However, the ball has been thrown 2 seconds after the first ball, so the actual time is

t = 11.3 + 2 = 13.3 s

This means that the first ball reaches the ground first.

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Answer:

For 5 s the ball will remain in air.

Explanation:

Given:

Displacement of the ball is equal to height of cliff, [tex]S=120\ m[/tex]

Acceleration of the ball is acceleration due to gravity, [tex]a=g=9.8\ m/s^2[/tex]

Assuming the ball is dropped from the top.

Hence, initial velocity of the ball is, [tex]u=0\ m/s[/tex]

Let 't' be the time the ball takes to reach the base of cliff.

Now, we have to use the Newton's equations of motion that relates displacement, initial velocity, acceleration and time.

So, we use the following equation of motion:

[tex]S=ut+\frac{1}{2}at^2[/tex]

Plug in the given values and solve for 't'. This gives,

[tex]120=0+\frac{1}{2}(9.8)t^2\\120=4.9t^2\\\frac{120}{4.9}=t^2\\t^2\approx25\\t=\sqrt{25}=5\ s[/tex]

Therefore, the time till the ball is in air is approximately 5 s.

Answer:

Because the chemical reaction cools down, releasing excessive heat into its surroundings, which we interpret as heat.

Explanation:

Answer:

Amplitude is the vertical distance between a ridge and the midpoint of the wave.

Explanation:

A mechanical wave is a disturbance that travels through a material or substance that is a medium of the wave. For example, when a tense string is pressed, the disturbance caused spreads along it in the form of a wave pulse. The disturbance in this case consists in the variation of The Shape of the string from its equilibrium state

it is important to know:

Crest: the crest is the highest point of this amplitude.

Period: the period is the time it takes the wave to go from one point of maximum amplitude to the next.

Amplitude: amplitude is the vertical distance between a crest and the midpoint of the wave.

Frequency: number of times that vibration is repeated.

Valley: it is the lowest point of a wave.

Wavelength: distance between two consecutive ridges of this size.

Transverse wave velocity.-

The propagation speed of a wave on a string (v) is proportional to the square root of the string tension (T) and inversely proportional to the square root of the linear density (μ) of the string:

[tex]v = \sqrt{\frac{T}{μ} }[/tex]

Answer:

A

Explanation:

When bacteria in the soil takes nitrogen from the air it becomes nitrates it can finally move through the food chain in this form.

Nitrogen enters the food web by means of nitrogen-fixing bacteria and algae in the soil.

Nitrogen is an important component of living organisms. The atoms of nitrogen are found in all strands of DNA and protein. The atmosphere nitrogen gas N₂ is converted into ammonia by bacteria. Ammonia is the usable product of nitrogen gas, utilized by plants. When animals eat the plants, they acquire nitrogen into usable compounds and hence, the nitrogen enters into the food web.

Nitrogen gas from the atmosphere is fixed into organic nitrogen by using nitrogen-fixing bacteria. This organic nitrogen enters into the terrestrial food webs. It leaves the food webs as the nitrogenous wastes in the soil. The nitrogen compounds present in soil by algae is the process called Eutrophication. Hence, the bacteria play a vital role in the conversion of nitrogen into ammonia.

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Answer:

The best options from the answer choises above would be Opption B.

Explanation:

Gravitational forces are equal in both directions.

good luck.

Answer:

[tex]\displaystyle \vec a=-\frac{0.5\vec v_o}{t}[/tex]

[tex]\displaystyle \vec F_{net}=-\frac{0.5\vec v_om}{t}[/tex]

[tex]\vec v_f-\vec v_o=-0.5\vec v_o[/tex]

Explanation:

Dynamics

The dynamics of an object on which a net force is applied are explained by Newton's laws. The net force equals the product of the mass of the object by its acceleration

[tex]\vec F_{net}=m\vec a[/tex]

The formulas for the accelerated motion gives us other relevant magnitudes like the velocity

[tex]\vec v_f=\vec v_o+\vec a\ t[/tex]

Since all the magnitudes are vectors, given an initial state and a final state, their average values only depend on the difference of their states.

We know during the move from A to B, and object decreases its veclocity by half. It means

[tex]\vec v_f=0.5\vec v_o[/tex]

It that happened in a time t, then the average acceleration was

[tex]\displaystyle \vec a=\frac{\vec v_f-\vec v_o}{t}[/tex]

[tex]\displaystyle \vec a=\frac{0.5\vec v_o-\vec v_o}{t}[/tex]

[tex]\displaystyle \vec a=-\frac{0.5\vec v_o}{t}[/tex]

If the object has a mass m, the net force is

[tex]\displaystyle \vec F_{net}=m\vec a=-m\ \frac{0.5\vec v_o}{t}[/tex]

[tex]\displaystyle \vec F_{net}=-\frac{0.5\vec v_om}{t}[/tex]

Finally, the average velocity was

[tex]\vec v_f-\vec v_o=-0.5\vec v_o[/tex]

Average acceleration can be found using Δv/Δt and is negative if the particle is slowing down. Average net force requires the particle's mass and acceleration, which is calculated using Newton's second law. Average velocity is zero if the net displacement is zero.

The question deals with finding the average acceleration, average net force (Fnet), and average velocity of a particle during a motion where the velocity decreases by half.

For the average acceleration, one would typically use the formula a_avg = Δv / Δt, where Δv is the change in velocity and Δt is the change in time. Since the velocity is decreasing and acceleration is given as negative when the particle is slowing down, the acceleration vector will also be negative.

To determine average Fnet, one could use Newton's second law, F = ma, once the mass of the object and the average acceleration are known. However, without the mass, we cannot calculate the average net force.

In terms of average velocity, it would be calculated as the total displacement divided by the total time. In a scenario where the net displacement is zero (such as a round trip), the average velocity would also be zero.

(O). The number of protons is equal to the number of electrons. None of the options is correct.

Atoms are the basic building blocks of matter. They are the smallest particles of an element that retain the chemical properties of that element. An atom consists of a nucleus, which is composed of positively charged protons and neutral neutrons, surrounded by a cloud of negatively charged electrons.

Atoms are electrically neutral, which means that the number of positively charged protons in the nucleus is equal to the number of negatively charged electrons in the electron cloud surrounding the nucleus. This balance of charges results in an overall neutral charge for the atom. The number of neutrons in an atom can vary, but it is not directly related to the number of protons and electrons. Neutrons are neutral particles that help to stabilize the nucleus, but they do not contribute to the overall charge of the atom.

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Answer:

Petroleum

Explanation:

Water has a boiling point of 100°C meaning it will start to boil once the temperature reach 100° Celsius meanwhile

Petroleum's boiling point will change based on which petroleum product it is.

For example

LPG (which is a petroleum product)will boil at 40°C.

Answer:

Petroleum

Explanation:

Answer: 27.791 meters

Explanation: The precision of a measure depends on the number of significative decimals that it has, so the number that is most exact is the one with more numbers after the decimal point, in this case, is the third option: 27.791 m

This one is the most exact because you know that the lenght is:

27 meters, 7 centimetrs and 9.1 milimeters

Answer:

B

Explanation:

Mass is the amount of matter in an object. Weight is the force of gravity on an object.

The electrical force exerted on the object at the top corner of the triangle is horizontally leftward, and its magnitude is approximately 3.487 N.

Part A: The direction of the electrical force exerted on the object at the top corner due to the two objects at the horizontal base of the triangle is horizontally leftward. Since the charges at the corners of the triangle are negative and the charges at the base are also negative, the electrical force will repel the top object in the opposite direction.

Part B: To determine the magnitude of the electrical force, we can use Coulomb's Law. The formula for Coulomb's Law is F = k * (q1 * q2) / r^2, where F is the force, k is the electric constant, q1 and q2 are the charges, and r is the distance between them.

In this case, both charges at the base of the triangle are -2.5 nC, and the distance between them and the top corner is 14 cm. Plugging in the values, we get F = (9 * 10^9 Nm^2/C^2) * ((-2.5 * 10^-9 C) * (-2.5 * 10^-9 C)) / (0.14 m)^2 ≈ 3.487 N.

Answer:

The four ligths will share the same voltage.

Explanation:

Parallel connected circuits stand out for sharing the same voltage between nodes, the voltage source is connected to two nodes and each node shares the same common point between lights.

In the attached image we can see four lights connected between two nodes, and sharing the same voltage of the voltage source.

Explanation:

I know that if the sun stopped shining, Earth would lose it's heat and we'd all freeze and die. On the other hand, we don't keep increasing temperature when the sun shines because heat escapes to space. But how does the heat leave earth's atmosphere if space is a vacuum and vacuums don't conduct heat except through waves

Earth would lose it's heat and we'd all freeze and die. On the other hand, we don't keep increasing temperature when the sun shines because heat escapes to space. But how does the heat leave earth's atmosphere if space is a vacuum and vacuums don't conduct heat except through waves

Explanation:

Answer:

Time = 0.64 s

Explanation:

Given:

Displacement of the storage cabinet is, [tex]S=2\ m[/tex]

As the object falls from the top, so initial velocity is, [tex]u=0\ m/s[/tex]

Also, the acceleration of the storage cabinet is due to gravity only.

So, acceleration of the storage cabinet is, [tex]a=9.8\ m/s^2[/tex]

Now, in order to find the time taken to reach the floor, we have to use the equation of motion that relates displacement, initial velocity, acceleration and time.

So, the equation of motion used is given as:

[tex]S=ut+\frac{1}{2}at^2[/tex]

Plug in the given values and solve for time 't'. This gives,

[tex]2=0+\frac{1}{2}(9.8)(t^2)\\\\2=4.9t^2\\\\t^2=\frac{2}{4.9}\\\\t^2=0.4082\\\\t=\sqrt{0.4082}\\\\t=0.64\ s[/tex]

Therefore, the storage cabinet takes 0.64 seconds to reach the floor.

Answer:

2.55 m

Explanation:

Elastic energy = gravitational energy

½ kx² = mgh

h = kx² / (2mg)

h = (200 N/m) (0.05 m)² / (2 × 0.010 kg × 9.8 m/s²)

h = 2.55 m

The height that the ball will assume is equal to 2.55 m

This is called the Law of Conservation of Energy. In the case of a hydroelectric plant, for example, water flows in the river at a certain speed and falls from a certain height, turning like turbines, which transform mechanical energy into electrical energy.

So, this is Elastic energy = gravitational energy, making the calculus we have:

[tex](1/2)kx^2 = mgh\\h = kx^2 / (2mg)\\h = (200 N/m) (0.05 m)^2 / (2 * 0.010 kg * 9.8 m/s^2)\\h = 2.55 m[/tex]

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Answer:

The answer is A)

Explanation:

The wall pushes back on you with the same force.

This is easily analyzed since when pushing or applying force toward the wall it does not move, it can be said that the system is in balance, this mathematically corresponds to that the sum of forces will be equal to zero, for this to be true the wall must apply an equal force and opposite to the force applied on the wall.

The above corresponds to newton's third law which says: Newton's Third Law also known as the principle of action and reaction tells us that if a body A exerts an action on another body B, it performs on another action-equal and of opposite sense.

An example of this can be seen in the attached image.

When you push against a brick wall, the wall pushes back with the same force, according to Newton's third law of motion.

When you push against a brick wall, according to Newton's third law of motion, the answer is A.) The wall pushes back on you with the same force. Newton's third law of motion states that for every action, there is an equal and opposite reaction.

This means that any force exerted on a body will produce a reaction force from the body that is equal in size but opposite in direction. Therefore, when you push on a brick wall, the wall pushes back with the same force, but the wall is firmly in place, due to its high mass and the friction between the wall and its foundation, which makes it seem immovable.

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Final answer:

OPTION D

As ocean waves reach shallower water and velocity decreases, the frequency remains the same and the wavelength decreases to adhere to the wave equation.

Explanation:

As ocean waves approach shore, their velocity decreases due to the interaction with the shallower sea floor. However, the frequency of the waves does not change because it is determined by the original energy source that created the waves, such as wind or seismic activity, and it remains consistent. Instead, when the velocity decreases, the wavelength of the waves must also decrease to maintain the same frequency. This phenomenon is described by the wave equation v = f × λ, where v is the velocity, f is the frequency, and λ (lambda) is the wavelength. Consequently, if the wave velocity decreases and the frequency remains constant, the equation dictates that the wavelength must also decrease. Therefore, the correct answer to the question is D: frequency stays the same and wavelength decreases.

Final answer:

As ocean waves approach the shore and slow down, the frequency remains unchanged and the wavelength decreases. The relationship is described by the equation v = fλ, where velocity decreases and frequency cannot change due to the wave's existing conditions.

Explanation:

As ocean waves approach the shore and their velocity decreases due to the shallower water, their frequency remains unchanged because it is determined by the original conditions that generated the wave. However, because the speed of the wave (or velocity) is the product of its frequency and wavelength, a decrease in velocity while maintaining the same frequency necessitates a corresponding decrease in wavelength. Therefore, the correct answer to how a decrease in velocity affects the frequency and wavelength of the waves entering shallow water is D. frequency stays the same and wavelength decreases.

Regarding other relationships between wave properties, it’s important to note that the frequency and wavelength of a wave are inversely related, as shown by the wave equation v = fλ, where v is the wave speed, f is the frequency, and λ (lambda) is the wavelength. Therefore, if the wave's speed decreases and its frequency cannot change due to the wave already being in existence, the wavelength must decrease. The idea that the frequency of the wave doesn't change when the wave moves from one medium to another is also true in other contexts, such as light traveling from air into water or glass.

Answer:

2.5 kg.m/s

Explanation:

Taking left side as positive while right side direction as negative then

Momentum, p= mv where m is the mass of the object and v is the velocity of travel

Momentum for ball moving towards right side=mv=2.5*-3=-7.5 kg.m/s

Momentum for the ball moving towards the left side=mv=2.5*4=10 kg.m/s

Total momentum=-7.5 kg.m/s+10 kg.m/s=2.5 kg.m/s

The total momentum of the two 2.5 kg balls moving in opposite directions is 2.5 kg×m/s, calculated by using the principle of conservation of momentum.

The question you're asking involves the conservation of momentum in physics. Momentum is defined as the product of the mass and velocity of an object. In a closed system where no external forces are involved, the total momentum of the objects before the event (collision, separation, etc.) is equal to the total momentum after the event.

In this case, two 2.5 kg balls are moving in opposite directions, one at 3 m/s and the other at 4 m/s. You can calculate the total momentum by adding together the momentum of each ball, taking into account their respective directions.

To find the magnitude of the total momentum of the system, you can use the formula: Total Momentum = Mass Ball 1 × Velocity Ball 1 (direction1) + Mass Ball 2 × Velocity Ball 2 (direction2). Since one ball is moving to the right and the other is moving to the left, we treat these directions as positive and negative respectively.

Therefore, the total momentum is: (2.5 kg × 3 m/s) - (2.5 kg × 4 m/s) = 7.5 kg×m/s - 10 kg×m/s = -2.5 kg × m/s. But, you're asking for the magnitude, so we take it as positive, which is 2.5 kg × m/s.

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Answer:

acceleration = 15.8 m/s^2

Explanation:

Weight of rocket which acts downward is W = mass × acceleration due to gravity

w = 30.9 × 9.81

W = 303.129 N

force of 790 N acts upward and it is greater than W hence acceleration is in upward direction and is given by Newton's second law of motion as

790 - W = mass × acceleration

790 - 303.129 = 30.9 × acceleration

486.871  = 30.9 × acceleration

acceleration = 486.871 / 30.9

acceleration = 15.756 m/s^2

acceleration = 15.8 m/s^2

Answer:

can I have a picture or like options

Explanation:

please , if you send them I'll edit answer

Velocity is an example of a vector quantity.

What is velocity ?

velocity is defined as rate of change of displacement of the object with respect to rate of change in time. In mathematics It is written as :

                                        [tex]\begin{aligned}v&=\frac{d_{2}-d{1}}{t_{2}-t_1}\end{aligned}[/tex]

velocity is nothing but speed in particular direction. That is velocity is vector quality having both magnitude and direction where as speed is just the magnitude of velocity.

Therefore, velocity is an example of a vector quantity and all other are scaler quality.

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Answer:

[tex]g=16.28m/s^2[/tex]

Explanation:

The gravitational acceleration on the surface of the earth is

[tex]g_{e}=\frac{Gm_{e}}{R_{e}^2}[/tex]

where G is the universal gravitational constant, [tex]m_{e}[/tex] is the mass of earth, and [tex]R_{e}[/tex] is the radius of earth,

in general for any object the gravitational acceleration or gravity on its surface is:

[tex]g=\frac{Gm}{R^{2}}[/tex]

in this case we know that the mass is 1.66 times the mass of earth:

[tex]m=1.66*m_{e}[/tex]

and the radius is the same as for earth:

[tex]R=R_{e}[/tex]

so the gravity for this planet is

[tex]g=\frac{G(1.66m_{e})}{R_{e}^2}[/tex]

which can be written in the following form:

[tex]g=(1.66)\frac{Gm_{e}}{R_{e}^2}[/tex]

where we know that [tex]g_{e}=\frac{Gm_{e}}{R_{e}^2}[/tex] , so:

[tex]g=(1.66)g_{e}[/tex]

and the acceleration of gravity on earth is: [tex]g_{e}=9.81m/s^2[/tex]

so the acceleration or gravity on the planet is:

[tex]g=(1.66)(9.81m/s^2)\\g=16.28m/s^2[/tex]

The gravity on the surface of a hypothetical planet with a mass of 1.66 times that of Earth and the same radius would be 1.66 times that on Earth, or approximately 16.28 m/s². Thus, the person would weigh about 1.66 times as much on this planet as they do on Earth.

The gravity on the surface of a hypothetical planet that has a mass of 1.66 times that of Earth but the same radius can be determined by the equation g = GM/r², where G is the gravitational constant, M is the mass of the object, and r is the radius.

Given that the mass (M) of this planet is 1.66 times that of Earth, and the radius (r) is the same, the gravitational force (g) will be 1.66 times that of Earth. On Earth, the average gravitational force at the surface is approximately 9.8 m/s². Therefore, for this hypothetical planet, the gravity would be approximately 1.66 * 9.8 = 16.28 m/s².

This means a person would weigh approximately 1.66 times as much on the surface of this planet as they do on Earth, assuming that their mass remains constant.

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Answer:

the new gravitational force between the two masses is [tex]\frac{3}{2}[/tex] of the original force (third option in the provided list)

Explanation:

Recall the expression for gravitational force : [tex]F_g=G\,\frac{m_A*\,m_B2}{d^2}[/tex], where [tex]m_A[/tex] and [tex]m_B[/tex] are the point masses, d the distance between them, and G the universal gravitational constant.

I our problem, the distant between the particles stays unchanged, and we need to know what happens with the magnitude of the force as mass A is tripled, and mass B is halved.

Initial force expression: [tex]F_i=G\,\frac{m_A\,m_B}{d^2}[/tex]

Final force expression: [tex]F_f=G\,\frac{3*m_A\,m_B/2}{d^2}\\F_f=G\,\frac{m_A\,m_B\,*\,3/2}{d^2}\\F_f=G\,\frac{m_A\,m_B}{d^2}\,*\frac{3}{2} \\F_f=F_i\,*\frac{3}{2}[/tex]

Where we have recognized the expression for the initial force between the particles, and replaced it with [tex]F_i[/tex] to make the new relation obvious.

Therefore, the new gravitational force between the two masses is [tex]\frac{3}{2}[/tex] of the original force.

Answer:

3/2 F is the Answer

Answer:

3750 N

Explanation:

Pressure on the small cylinder = pressure on the large cylinder

P₁ = P₂

F₁ / A₁ = F₂ / A₂

F₁ / (π d₁² / 4) = F₂ / (π d₂² / 4)

F₁ / d₁² = F₂ / d₂²

600 N / (10.0 cm)² = F / (25.0 cm)²

F = 3750 N

Answer:

3751.34N

Explanation:

Pressure in large piston = pressure in smaller piston

P2 = P1

Pressure = Force / Area

Area = pi * r²

r1= d1/2 = 10/ 2 = 5cm = 0.05m

Area(A1) = 22/7 * (0.05)² = 0.00785m²

r2 = d2 / 2 = 25/2 = 12.5cm = 0.125m

Area(A2) = 22/7 * (0.125)² = 0.04908m²

Pressure = Force / Area

F1/A1 = F2/A2

600 / 0.00785 = F2 / 0.04908

F2 = (600 * 0.04908) / 0.00785

F2 = 3751.34N

Answer:

Forces affect how objects move. They may cause motion; they may also slow, stop, or change the direction of motion of an object that is already moving. Since force cause changes in the speed or direction of an object, we can say that forces cause changes in velocity. ... So forces cause acceleration.

Answer:

Its called force

Explanation:

Answer:

F = N*μ or F =m*g*μ

Explanation:

The friction force is defined as the product of the normal force by the corresponding friction factor.

When a body is in equilibrium over a horizontal plane its normal force value shall be equal to:

[tex]N = m*g\\where:\\m=mass [kg]\\g=gravity [m/s^2]\\N= normal force [N][/tex]

if we simplify this formula more for a balanced body on a horizontal plane, we will have.

[tex]F=m*g*u[/tex]

The magnitude of the frictional force along a plane depends on the normal force and the coefficient of friction between the two surfaces. The force opposes motion in scenarios involving inclines or sliding objects and can be adjusted using the object's weight components and the coefficients of friction. In cases of rolling motion without slipping, the static friction force helps keep the object rolling smoothly.

The magnitude of the frictional force along a plane is determined by the normal force (the force exerted by the surface) and the coefficient of friction between both surfaces. This friction force can oppose the motion on a surface which inclines in the case of a skier or a sliding block as mentioned in the examples. To calculate it, you would multiply the normal force (N) by the coefficient of friction (µ). For example, in a scenario where a block is sliding on a horizontal surface, if the gravitational force is 40N and the coefficient of friction is 0.20, then the magnitude of the frictional force would be 40N x 0.20 = 8N.

If the plane is inclined, you must project the object’s weight into components that are parallel and perpendicular to the surface. For instance, the normal force would be perpendicular and the frictional force parallel to the slope. The magnitude of the frictional force (f) is less than the component of the object's weight that is parallel to the slope (W ||), causing it to accelerate downslope. This can be adjusted using coefficients of friction and weight components.

In the case of a cylinder rolling without slipping, the rolling motion is due to the static friction force, and thus, the magnitude of this force would be less than or equal to the product of the static friction coefficient (µs) and the normal force (N). This keeps the cylinder rolling without skidding.

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Answer:

D. remains constant throughout the fall.

Explanation:

Horizontal Launching

We can launch an object in free air in three forms: vertically, horizontally or inclined. In any case, the only acting force to modify the object's velocity and make it go back to the ground is the force of gravity and it's always directed downwards. Unless friction or air resistance is considered, the horizontal motion is not affected because no force is acting in that direction.

The rock described in the question was launched at 3 m/s pointed horizontally. Immediately after launching, the rock starts to fall to the ground and gain vertical velocity, but the horizontal component remains the same until it completes the flight.  

The D option is correct: the horizontal velocity of the rock remains constant throughout the fall